per_tdlms.m

System identification with adaptive filter using full and partial-update Transform-Domain Least-Mean

function [e,w] = per_tdlms(x,d,N,S,w0,mu,lambda,epsilon)
%[e,w] = per_tdlms(x,d,N,S,w0,mu,lambda,epsilon) implements the
%periodic-partial-update TD-LMS algorithm using DCT and single-division
%power normalization.  
%   ----------------
%   input parameters
%   ----------------
%   x : Lx1 input signal
%   d : Lx1 desired response 
%   N : filter length
%   S : update period
%   w0 : Nx1 initialization
%   mu : step-size parameter
%   lambda : exponential forgetting factor for power estimation
%   epsilon : initialization for power estimate
%   ----------------
%   function outputs
%   ----------------
%   w : LxN evolution of coefficients
%   e : Lx1 error vector

x = x(:);
d = d(:);
w0 = w0(:);

L = length(x);
w = zeros(L,N);
e = zeros(L+S,1);

w(1,:) = w0';
xvec = zeros(N,1);

rpk = (1/epsilon)*ones(N,1);    %initial inv power estimate for single-division power normalization

invlambda = 1/lambda;

for i = 1:S:L
    for j = i:i+S-1
        xvec = x(j:-1:max([j-N+1,1]));
        xvec = [xvec;zeros(N-length(xvec),1)];
        vvec = dct(xvec);
        e(j) = d(j) - w(i,:)*vvec;
    end
    
    xvec = x(i:-1:max([i-N+1,1]));
    xvec = [xvec;zeros(N-length(xvec),1)];
    vvec = dct(xvec);

    bk = invlambda*rpk;
    ck = bk.*vvec; 
    upd = mu * e(i) * ck ;           %delayed normalized v
    ck = ck.* vvec;
    dk = bk.*ck;
    rpk = bk - dk/(1+sum(ck));      %update reciprocal power estimate
    
    w(i+S,:) = w(i,:) + upd';
end

e = e(1:L);